   Chapter 7.4, Problem 73E

Chapter
Section
Textbook Problem

# Suppose that F, G, and Q are polynomials and F ( x ) Q ( x ) = G ( x ) Q ( x ) for all x except when Q ( x ) = 0. Prove that F ( x ) = G ( x ) for all x. [Hint: Use continuity.]

To determine

To Prove:F(x)=G(x), given that F(x),G(x),Q(x) are polynomials and F(x)Q(x)=G(x)Q(x) for all x except at Q(x)=0

Explanation

Calculation: To Prove F(x)=G(x), we use the definition of continuity

Consider any point x=x0 such that Q(x0)0, then

F(x0)Q(x0)=G(x0)Q(x0)F(x0)=G(x0)

Consider any point x=x1 such that Q(x1)=0, then by using the definition of continuity of F(x),G(x),Q(x) [F(x),G(x),Q(x) are continuous as all polynomials are continuous]

limxx1F(x)=F(x1)limxx1G(x)=G(x1)

Consider limxx1[F(

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